Mathematical Sciences: Systems of Degenerate Partial Differential Equations of Ellipitic-Parabolic Type

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This project will analyse systems of nonlinear degenerate partial differential equations of elliptic-parabolic type which arise in modelling the combined flow of heat and electric current in a metallic conductor, the welding of metal sheets, and biological groups the dispersal of avoid crowding. Recent findings indicate that the existence assertion for these systems is closely tied to the size of the sets where the equations involved become degenerate. Equations in which the degeneracy causes the appearance of two free boundaries will also be studied.